Crystallization of supercooled water: A level-set-based modeling of the dendrite tip velocity

Abstract

It is well-known that solidification front of a supercooled liquid is unstable; consequently, this instability leads to the appearance of an array of dendrites of sub-micron diameter. The shape and the velocity of the dendrite propagation are determined by the thermodynamic properties of the liquid and solid phases, including interfacial energy as well as the initial temperatures of both. Accordingly, the numerical simulation of solidification process is a rather challenging problem which requires an accurate prediction of high temperature gradients near the moving solidification front. In this study a relevant level set formulation has been developed enabling correct determination of the position and the curvature of the liquid/ solid interface. At this interface a Dirichlet boundary condition for the temperature field is imposed by applying a ghost-face method. For the purpose of updating the level set function and optimizing computing time a narrow-band around the interface is introduced. Within this band, whose width is temporally adjusted to the maximum curvature of the interface, the normal-to-interface velocity is appropriately expanded. The computational model is firstly validated along with the analytical solution of stable freezing. The tip velocity of dendritic patterns (pertinent to unstable freezing) is investigated by performing two-dimensional simulations. The computational results exhibit excellent qualitative and quantitative agreement with the marginal stability theory as well as with the available experiments in the heat-diffusion-dominated region.

Towards modelling of initial and final stages of supercooled water solidification

“…The solid line in Fig. 5 represents the dimensionless steady-growth speed of freely growing ice crystals obtained theoretically as a function of the dimensionless supercooling [7].…”

“…[7,31] has been correspondingly modified towards fulfilment of an appropriate accuracy level with respect to the thermal energy equation discretization and the approximation of the temperature normal derivative close to the interface.…”

“…In the present work, a computational model based on the level set technique [27] used in Refs. [6,7,31] has been appropriately modified, aiming at increasing the accuracy level of the discretization of the equation governing the thermal energy and the normal-to-interface derivative of the temperature field. The model describes the freezing mechanism under supercooled conditions, relying on the physical and mathematical description of the twophase moving-boundary approach (minimal model of solidification) considering kinetic effects.…”

“…The relevant numerical algorithm is implemented into the open source software OpenFOAM ® and is based on the algorithm presented in Ref. [7].…”

A phase-field/ALE method for simulating fluid–structure interactions in two-phase flow

“…The phase-field approach [22,23,24,25,26,27,28] enjoys several advantages in handling two-phase flow among other available methods, i.e., level-set, volume-of-fluids, or front tracking [29,30,31,32,33,34]. First, it is based on the minimization of the free energy and hence it can handle moving contact lines and deal with morphological changes of the interface.…”